Complex acoustic resonance speech analysis system

ABSTRACT

A method and apparatus are provided for determining an instantaneous frequency and an instantaneous bandwidth of a speech resonance of a speech signal. The method includes receiving a speech signal having a real component; filtering the speech signal so as to generate a plurality of filtered signals such that the real component and an imaginary component of the speech signal are reconstructed; and generating a first estimated frequency and a first estimated bandwidth of a speech resonance of the speech signal based on both a first filtered signal of the plurality of filtered signals and a single-lag delay of the first filtered signal.

TECHNICAL FIELD

The present invention relates generally to the field of speechrecognition, and more particularly to systems for speech recognitionsignal processing and analysis.

BACKGROUND

Modern human communication increasingly relies on the transmission ofdigital representations of acoustic speech over large distances. Thisdigital representation contains only a fraction of the information aboutthe human voice, and yet humans are perfectly capable of understanding adigital speech signal.

Some communication systems, such as automated telephone attendants andother interactive voice response systems (IVRs), rely on computers tounderstand a digital speech signal. Such systems recognize the sounds aswell as the meaning inherent in human speech, thereby extracting thespeech content of a digitized acoustic signal. In the medical and healthcare fields, correctly extracting speech content from a digitizedacoustic signal can be a matter of life or death, making accurate signalanalysis and interpretation particularly important.

One approach to analyzing a speech signal to extract speech content isbased on modeling the acoustic properties of the vocal tract duringspeech production. Generally, during speech production, theconfiguration of the vocal tract determines an acoustic speech signalmade up of a set of speech resonances. These speech resonances can beanalyzed to extract speech content from the speech signal.

In order to determine accurately the acoustic properties of the vocaltract during speech production, both the frequency and the bandwidth ofeach speech resonance are required. Generally, the frequency correspondsto the size of the cavity within the vocal tract, and the bandwidthcorresponds to the acoustic losses of the vocal tract. Together, thesetwo parameters determine the formants of speech.

During speech production, speech resonance frequency and bandwidth maychange quickly, on the order of a few milliseconds. In most cases, thespeech content of a speech signal is a function of sequential speechresonances, so the changes in speech resonances must be captured andanalyzed at least as quickly as they change. As such, accurate speechanalysis requires simultaneous determination of both the frequency andbandwidth of each speech resonance on the same time scale as speechproduction, that is, on the order of a few milliseconds. However, thesimultaneous determination of frequency and bandwidth of speechresonances on this time scale has proved difficult.

Some previous work in formant estimation has been concerned with findingonly the frequency of speech resonances in speech signals. Thesefrequency-oriented methods use the instantaneous frequency for hightime-resolution frequency estimates. However, these methods forfrequency estimation are limited in flexibility, and do not fullydescribe the speech resonances.

For example, Nelson, et al., have developed a number of methods,including U.S. Pat. No. 6,577,968 for a “Method of estimating signalfrequency,” on Jun. 10, 2003, by Douglas J. Nelson; U.S. Pat. No.7,457,756 for a “Method of generating time-frequency signalrepresentation preserving phase information,” on Nov. 25, 2008, byDouglas J. Nelson and David Charles Smith; and U.S. Pat. No. 7,492,814for a “Method of removing noise and interference from signal using peakpicking,” on Feb. 17, 2009, by Douglas J. Nelson.

Generally, systems consistent with the Nelson methods (“Nelson-typesystems”) use instantaneous frequency to enhance the calculation of aShort-Time Fourier Transform (STFT), a common transform in speechprocessing. In Nelson-type systems, the instantaneous frequency iscalculated as the time-derivative of the phase of a complex signal. TheNelson-type systems approach computes the instantaneous frequency fromconjugate products of delayed whole spectra. Having computed theinstantaneous frequency of each time-frequency element in the STFT, theNelson-type systems approach re-maps the energy of each element to itsinstantaneous frequency. This Nelson-type re-mapping results in aconcentrated STFT, with energy previously distributed across multiplefrequency bands clustering around the same instantaneous frequency.

Auger & Flandrin also developed an approach, which is described in: F.Auger and P. Flandrin, “Improving the readability of time-frequency andtime-scale representations by the reassignment method,” SignalProcessing, IEEE Transactions on 43, no. 5 (May 1995): 1068-1089(“Auger/Flandrin”). Systems consistent with the Auger/Flandrin approach(“Auger/Flandrin-type systems”) offer an alternative to the concentratedShort-Time Fourier Transform (STFT) of Nelson-type systems. Generally,Auger/Flandrin-type systems compute several STFTs with differentwindowing functions. Auger/Flandrin-type systems use the derivative ofthe window function in the STFT to get the time-derivative of the phase,and the conjugate product is normalized by the energy.Auger/Flandrin-type systems yield a more exact solution for theinstantaneous frequency than the Nelson-type systems' approach, as thederivative is not estimated in the discrete implementation.

However, as extensions of STFT approaches, both Nelson-type andAuger/Flandrin-type systems lack the necessary flexibility to modelhuman speech effectively. For example, the transforms of bothNelson-type and Auger/Flandrin-type systems determine window length andfrequency spacing for the entire STFT, which limits the ability tooptimize the filter bank for speech signals. Moreover, while both typesfind the instantaneous frequencies of signal components, neither typefinds the instantaneous bandwidths of the signal components. As such,both the Nelson-type and Auger/Flandrin-type approaches suffer fromsignificant drawbacks that limit their usefulness in speech processing.

Gardner and Mognasco describe an alternate approach in: T. J. Gardnerand M. O. Magnasco, “Instantaneous frequency decomposition: Anapplication to spectrally sparse sounds with fast frequencymodulations,” The Journal of the Acoustical Society of America 117, no.5 (2005): 2896-2903 (“Gardner/Mognasco”). Systems consistent with theGardner/Mognasco approach (“Gardner/Mognasco-type systems”) use ahighly-redundant complex filter bank, with the energy from each filterremapped to its instantaneous frequency, similar to the Nelson approachabove. Gardner/Mognasco-type systems also use several other criteria tofurther enhance the frequency resolution of the representation.

That is, the Gardner/Mognasco-type systems discard filters with a centerfrequency far from the estimated instantaneous frequency, which canreduce the frequency estimation error from filters not centered on thesignal component frequency. Gardner/Mognasco-type systems also use anamplitude threshold to remove low-energy frequency estimates andoptimize the bandwidths of filters in a filter bank to maximize theconsensus of the frequency estimates of adjacent filters.Gardner/Mognasco-type systems then use consensus as a measure of thequality of the analysis, where high consensus across filters indicates agood frequency estimate.

However, Gardner/Mognasco-type systems also suffer from significantdrawbacks. First, Gardner/Mognasco-type systems do not account forinstantaneous bandwidth calculation, thus missing an important part ofthe speech formant. Second, a consensus approach can lock in an errorwhen a group of frequency estimates are briefly consistent with eachother, but nevertheless provide inaccurate estimates of the trueresonance frequency. For both of these reasons, Gardner/Mognasco-typesystems offer limited usefulness in speech processing applications,particularly those applications that require higher accuracy over ashort time scale.

While the above methods attempt to determine instantaneous frequencywithout also determining instantaneous bandwidth, Potamianos and Maragosdeveloped a method for obtaining both the frequency and bandwidth offormants of a speech signal. The Potamianos/Maragos approach isdescribed in: Alexandros Potamianos and Petros Maragos, “Speech formantfrequency and bandwidth tracking using multiband energy demodulation,”The Journal of the Acoustical Society of America 9, no. 6 (1996):3795-3806 (“Potamianos/Maragos”).

Systems consistent with the Potamianos/Maragos approach(“Potamianos/Maragos-type systems”) use a filter bank of real-valuedGabor filters, and calculate the instantaneous frequency at eachtime-sample using an energy separation algorithm to demodulate thesignal into an instantaneous frequency and amplitude envelope. InPotamianos/Maragos-type systems, the instantaneous frequency is thentime-averaged to give a short-time estimate of the frequency, with atime window of about 10 ms. In Potamianos/Maragos-type systems, thebandwidth estimate is simply the standard deviation of the instantaneousfrequency over the time window.

Thus, while Potamianos/Maragos-type systems offer the flexibility of afilter bank (rather than a transform), Potamianos/Maragos-type systemsonly indirectly estimate the instantaneous bandwidth by using thestandard deviation. That is, because the standard deviation requires atime average, the bandwidth estimate in Potamianos/Maragos-type systemsis not instantaneous. Because the bandwidth estimate is notinstantaneous, the frequency and bandwidth estimates must be averagedover longer times than are practical for real-time speech recognition.As such, the Potamianos/Maragos-type systems also fail to determinespeech formants on the time scale preferred for real-time speechprocessing.

SUMMARY

In brief, the disclosed method determines an instantaneous frequency andan instantaneous bandwidth of a speech resonance of a speech signal.Having received a speech signal, a reconstruction module filters thespeech signal, generating a plurality of filtered signals. In eachfiltered signal, the real component and an imaginary component of thespeech signal are reconstructed. A single-lag delay of the speech signalis also formed, based on a selected filtered signal. The estimatedfrequency and bandwidth of a speech resonance of the speech signal aregenerated based on both the selected filtered signal and the single-lagdelay of the first filtered signal.

In one general aspect of the invention, a method is provided fordetermining an instantaneous frequency and an instantaneous bandwidth ofa speech resonance of a speech signal. The method includes receiving aspeech signal having a real component; filtering the speech signal so asto generate a plurality of filtered signals such that the real componentand an imaginary component of the speech signal are reconstructed; andgenerating a first estimated frequency and a first estimated bandwidthof a speech resonance of the speech signal based on a first filteredsignal of the plurality of filtered signals and a single-lag delay ofthe first filtered signal.

In a preferred embodiment, filtering is performed by a filter bankhaving a plurality of complex filters, each complex filter generatingone of the plurality of filtered signals. In another preferredembodiment, the method also includes generating a plurality of estimatedfrequencies and a plurality of estimated bandwidths, based on theplurality of filtered signals and a plurality of single-lag delays ofthe plurality of filtered signals.

In yet another preferred embodiment, the filter bank includes aplurality of finite impulse response (FIR) filters. In another preferredembodiment, the filter bank includes a plurality of infinite impulseresponse (IIR) filters. In still another preferred embodiment, thefilter bank includes a plurality of complex gammatone filters.

In still another preferred embodiment, each complex filter includes afirst selected bandwidth and a first selected center frequency. Inanother preferred embodiment, each complex filter comprises: a selectedbandwidth of a plurality of bandwidths, the plurality of bandwidthsbeing distributed within a first predetermined range; and a selectedcenter frequency of a plurality of center frequencies, the plurality ofcenter frequencies being distributed within a second predeterminedrange.

In another preferred embodiment, each complex filter comprises a firstselected bandwidth and a first selected center frequency, the firstselected bandwidth and first selected center frequency being configuredto optimize analysis accuracy.

In another general aspect of the invention, a method is provided fordetermining an instantaneous frequency and an instantaneous bandwidth ofa speech resonance of a speech signal. The method includes: receiving aspeech signal having a real component; filtering the speech signal so asto generate a plurality of filtered signals such that the real componentand an imaginary component of the speech signal are reconstructed;forming a first integrated-product set, the forming being performed byan integration kernel, the first integrated-product set being based on afirst filtered signal of the plurality of filtered signals, and thefirst integrated-product set having: at least one zero-lag complexproduct and at least one single-lag complex product; and generating,based on the first integrated-product set, a first estimated frequencyand a first estimated bandwidth of a speech resonance of the speechsignal. In a preferred embodiment, the integration kernel is a secondorder gamma IIR filter.

In another preferred embodiment, the method also includes: forming aplurality of integrated-product sets, each integrated-product set beingbased on one of the plurality of filtered signals, and eachintegrated-product set having: at least one zero-lag complex product andat least one single-lag complex product; and generating, based on theplurality of integrated-product sets, a plurality of estimatedfrequencies and a plurality of estimated bandwidths.

In yet another preferred embodiment, the filter bank includes aplurality of finite impulse response (FIR) filters. In another preferredembodiment, the filter bank includes a plurality of infinite impulseresponse (IIR) filters. In still another preferred embodiment, thefilter bank includes a plurality of complex gammatone filters. Inanother preferred embodiment, each complex filter generates one of theplurality of filtered signals.

In still another preferred embodiment, each complex filter includes afirst selected bandwidth and a first selected center frequency. Inanother preferred embodiment, each complex filter comprises: a selectedbandwidth of a plurality of bandwidths, the plurality of bandwidthsbeing distributed within a first predetermined range; and a selectedcenter frequency of a plurality of center frequencies, the plurality ofcenter frequencies being distributed within a second predeterminedrange. In another preferred embodiment, each complex filter comprises afirst selected bandwidth and a first selected center frequency, thefirst selected bandwidth and first selected center frequency beingconfigured to optimize analysis accuracy.

In yet another preferred embodiment, wherein the first filtered signalis formed by a first filter having a first selected bandwidth and afirst center frequency, the method further includes generating a secondestimated frequency and a second estimated bandwidth, the generatingbeing based on a second filtered signal of the plurality of filteredsignals, the second filtered signal being formed by a second filterhaving a second selected bandwidth and a second center frequency; andgenerating a third estimated bandwidth, the generating being based on:the first and second estimated frequencies, the first selectedbandwidth, and the first and second center frequencies.

In still another preferred embodiment, wherein the first filtered signalis formed by a first filter having a first selected bandwidth and afirst center frequency, the method further includes generating a secondestimated frequency and a second estimated bandwidth, the generatingbeing based on a second filtered signal of the plurality of filteredsignals, the second filtered signal being formed by a second filterhaving a second selected bandwidth and a second center frequency; andgenerating a third estimated bandwidth, the generating being based on:the first and second estimated frequencies, the first selectedbandwidth, and the first and second center frequencies; and generating athird estimated frequency, the generating being based on: the thirdestimated bandwidth, the first estimated frequency, the first selectedfrequency, and the first selected bandwidth.

In another general aspect of the invention, a method is provided fordetermining an instantaneous frequency and an instantaneous bandwidth ofa speech resonance of a speech signal. The method includes receiving aspeech signal having a real component. The speech signal is filtered soas to generate a plurality of filtered signals such that the realcomponent and an imaginary component of the speech signal arereconstructed. A first integrated-product set is formed by anintegration kernel, the first integrated-product set being based on afirst filtered signal of the plurality of filtered signals. The firstintegrated-product set has at least one zero-lag complex product and atleast one two-or-more-lag complex product. Based on the firstintegrated-product set, a first estimated frequency and a firstestimated bandwidth of a speech resonance of the speech signal aregenerated.

In a preferred embodiment, the method includes forming a plurality ofintegrated-product sets, each integrated-product set being based on oneof the plurality of filtered signals, and each integrated-product sethaving: at least one zero-lag complex product, and at least onetwo-or-more-lag complex product. Based on the plurality ofintegrated-product sets, a plurality of estimated frequencies and aplurality of estimated bandwidths are generated.

In another preferred embodiment, filtering is performed by a filter bankhaving a plurality of finite impulse response (FIR) filters. In yetanother preferred embodiment, filtering is performed by a filter bankhaving a plurality of infinite impulse response (IIR) filters. In stillanother preferred embodiment, filtering is performed by a filter bankhaving a plurality of complex gammatone filters. In yet anotherpreferred embodiment, filtering is performed by a filter bank having aplurality of complex filters, each complex filter generating one of theplurality of filtered signals.

In still another preferred embodiment, filtering is performed by afilter bank having a plurality of complex filters, each complex filterhaving a first selected bandwidth and a first selected center frequency.In yet another preferred embodiment, filtering is performed by a filterbank having a plurality of complex filters. In one preferred embodiment,each complex filter has a selected bandwidth of a plurality ofbandwidths, the plurality of bandwidths being distributed within a firstpredetermined range, and a selected center frequency of a plurality ofcenter frequencies, the plurality of center frequencies beingdistributed within a second predetermined range. In another preferredembodiment, each complex filter has a selected bandwidth of a pluralityof bandwidths, the selected bandwidth being configured to optimizeanalysis accuracy, and a selected center frequency of a plurality ofcenter frequencies, the selected center frequency being configured tooptimize analysis accuracy.

In another general aspect of the invention, a method is provided fordetermining an instantaneous frequency and an instantaneous bandwidth ofa speech resonance of a speech signal. The method includes generating afirst estimated frequency and a first estimated bandwidth of the speechresonance based on a first filtered signal, the first filtered signalbeing formed by a first complex filter having a first selected bandwidthand a first center frequency. The method includes generating a secondestimated frequency and a second estimated bandwidth of the speechresonance based on a second filtered signal, the second filtered signalbeing formed by a second complex filter having a second selectedbandwidth and a second center frequency. The method also includesgenerating a third estimated bandwidth of the speech resonance, thegenerating being based on: the first and second estimated frequencies,the first selected bandwidth, and the first and second centerfrequencies.

In a preferred embodiment, the method includes generating a thirdestimated frequency of the speech resonance, the generating being basedon: the third estimated bandwidth, the first estimated frequency, thefirst center frequency, and the first selected bandwidth.

In another general aspect of the invention, an apparatus is presented,the apparatus configured for determining an instantaneous frequency andan instantaneous bandwidth of a speech resonance of a speech resonancesignal. The apparatus includes a reconstruction module configured toreceive a speech resonance signal having a real component. Thereconstruction module is further configured to filter the speechresonance signal so as to generate a plurality of filtered signals suchthat the real component and an imaginary component of the speechresonance signal are reconstructed. An estimator module couples to thereconstruction module, the estimator module being configured to generatea first estimated frequency and a first estimated bandwidth of a speechresonance of the speech resonance signal based on a first filteredsignal of the plurality of filtered signals and a single-lag delay ofthe first filtered signal.

In a preferred embodiment, the reconstruction module includes a filterbank having a plurality of complex filters, and each complex filter isconfigured to generate one of the plurality of filtered signals. Inanother preferred embodiment, the estimator module is further configuredto generate a plurality of estimated frequencies and a plurality ofestimated bandwidths, based on the plurality of filtered signals and aplurality of single-lag delays of the plurality of filtered signals.

In still another preferred embodiment, the reconstruction moduleincludes a plurality of finite impulse response (FIR) filters. Inanother preferred embodiment, the reconstruction module includes aplurality of infinite impulse response (IIR) filters. In anotherpreferred embodiment, the reconstruction module includes a plurality ofcomplex gammatone filters.

In yet another preferred embodiment, the reconstruction module includesa plurality of complex filters, each complex filter having a firstselected bandwidth and a first selected center frequency. In anotherpreferred embodiment, each complex filter comprises: a selectedbandwidth of a plurality of bandwidths, the plurality of bandwidthsbeing distributed within a first predetermined range; and a selectedcenter frequency of a plurality of center frequencies, the plurality ofcenter frequencies being distributed within a second predeterminedrange. In another preferred embodiment, each complex filter comprises: afirst selected bandwidth and a first selected center frequency, thefirst selected bandwidth and first selected center frequency beingconfigured to optimize analysis accuracy.

BRIEF DESCRIPTION OF THE DRAWINGS

The embodiments described herein will be more fully understood byreference to the detailed description, in conjunction with the followingfigures, wherein:

FIG. 1 a is a cutaway view of a human vocal tract;

FIG. 1 b is a high-level block diagram of a speech processing systemthat includes a complex acoustic resonance speech analysis system;

FIG. 2 is a block diagram of an embodiment of the speech processingsystem of FIG. 1 b, highlighting signal transformation and processorganization;

FIG. 3 is a block diagram of an embodiment of a speech resonanceanalysis module of the speech processing system of FIG. 2;

FIG. 4 is a block diagram of an embodiment of a complex gammatone filterof a speech resonance analysis module;

FIG. 5 is a high-level flow diagram depicting operational steps of aspeech processing method; and

FIGS. 6-9 are high-level flow diagrams depicting operational steps ofembodiments of complex acoustic speech resonance analysis methods.

DETAILED DESCRIPTION

FIG. 1 a illustrates a cutaway view of a human vocal tract 10. As shown,vocal tract 10 produces an acoustic wave 12. The qualities of acousticwave 12 are determined by the configuration of vocal tract 10 duringspeech production. Specifically, as illustrated, vocal tract 10 includesfour resonators 1, 2, 3, 4 that each contribute to generating acousticwave 12. The four illustrated resonators are the pharyngeal resonator 1,the oral resonator 2, the labial resonator 3, and the nasal resonator 4.All four resonators, individually and together, create speech resonancesduring speech production. These speech resonances contribute to form theacoustic wave 12.

FIG. 1 b illustrates an example of a speech processing system 100, inaccordance with one embodiment of the invention. Broadly, speechprocessing system 100 operates in three general stages, “input captureand pre-processing,” “processing and analysis,” and “post-processing.”Each stage is described in additional detail below.

To analyze and interpret a speech signal, some speech must first becaptured. The first stage is therefore, generally, “input capture andpre-processing.” As illustrated, speech processing system 100 isconfigured to capture acoustic wave 12, originating from vocal tract 10.As described above, a human vocal tract generates resonances in avariety of locations. In this stage, vocal tract 10 generates acousticwave 12. Input processing module 110 detects, captures, and convertsacoustic wave 12 into a digital speech signal.

More specifically, an otherwise conventional input processing module 110captures the acoustic wave 12 through an input port 112. Input port 112is an otherwise conventional input port and/or device, such as aconventional microphone or other suitable device. Input port 112captures acoustic wave 12 and creates an analog signal 114 based on theacoustic wave.

Input processing module 110 also includes a digital distribution module116. In one embodiment, digital distribution module 116 is an otherwiseconventional device or system configured to digitize and distribute aninput signal. As shown, digital distribution module 114 receives analogsignal 114 and generates an output signal 120. In the illustratedembodiment, the output signal 120 is the output of input processingmodule 110.

The speech resonance analysis module 130 of the invention describedherein receives the speech signal 120, forming an output signal suitablefor additional speech processing by post processing module 140. Asdescribed in more detail below, speech resonance analysis module 130reconstructs the speech signal 120 into a complex speech signal. Usingthe reconstructed complex speech signal, speech resonance analysismodule 130 estimates the frequency and bandwidth of speech resonances ofthe complex speech signal, and can correct or further process the signalto enhance accuracy.

Speech resonance analysis module 130 passes its output to a postprocessing module 140, which can be configured to perform a wide varietyof transformations, enhancements, and other post-processing functions.In some embodiments, post processing module 140 is an otherwiseconventional post-processing module. The following figures provideadditional detail describing the invention.

FIG. 2 presents the processing and analysis stage in a representationcapturing three broad sub-stages: reconstruction, estimation, andanalysis/correction. Specifically, FIG. 2 shows another view of system100. Input processing module 110 receives a real, analog, acousticsignal (i.e., a sound, speech, or other noise), captures the acousticsignal, converts it to a digital format, and passes the resultant speechsignal 120 to speech resonance analysis module 130.

One skilled in the art will understand that an acoustic resonance fieldsuch as human speech can be modeled as a complex signal, and thereforecan be described with a real component and an imaginary component.Generally, the input to input processing module 110 is a real, analogsignal from, for example, point 102 of FIG. 1, having lost the complexinformation during transmission. As shown, the output signal of module110, speech signal 120 (shown as X), is a digital representation of theanalog input signal, and lacks some of the original signal information.

Speech signal 120 (signal X) Is the input to the three stages ofprocessing of the invention disclosed herein, referred to herein as“speech resonance analysis.” Specifically, reconstruction module 210receives and reconstructs signal 120 such that the imaginary componentand real components of each resonance are reconstructed. This stage isdescribed in more detail below with respect to FIGS. 3 and 4. As shown,the output of reconstruction module 210 is a plurality of reconstructedsignals Y_(n), which each include a real component, Y_(R), and animaginary component, Y_(I).

The output of the reconstruction module 210 is the input to the nextbroad stage of processing of the invention disclosed herein.Specifically, estimator module 220 receives signals Y_(n), which is theoutput of the reconstruction stage. Very generally, estimator module 220uses the reconstructed signals to estimate the instantaneous frequencyand the instantaneous bandwidth of one or more of the individual speechresonances of the reconstructed speech signal. This stage is describedin more detail below with respect to FIG. 3. As shown, the output ofestimator module 220 is a plurality of estimated frequencies({circumflex over (f)}_(1 . . . n)) and estimated bandwidths({circumflex over (β)}_(1 . . . n)).

The output of the estimator module 220 is the input to the next broadstage of processing of the invention disclosed herein. Specifically,analysis & correction module 230 receives the plurality of estimatedfrequencies and bandwidths that are the output of the estimation stage.Very generally, module 230 uses the estimated frequencies and bandwidthsto generate revised estimates. In one embodiment, the revised estimatedfrequencies and bandwidths are the result of novel corrective methods ofthe invention. In an alternate embodiment, the revised estimatedfrequencies and bandwidths, themselves the result of novel estimationand analysis methods, are passed to a post-processing module 240 forfurther refinement. This stage is described in more detail with respectto FIG. 3.

Generally, as described in more detail below, the output of the analysisand correction module 230 provides significant improvements over priorart systems and methods for estimating speech resonances. Configured inaccordance with the invention described herein, a speech processingsystem can produce, and operate on, more accurate representations ofhuman speech. Improved accuracy in capturing these formants results inbetter performance in speech applications relying on thoserepresentations.

More particularly, the invention presented herein determines individualspeech resonances with a multi-channel, parallel processing chain thatuses complex numbers throughout. Based on the properties of acousticresonances, the invention is optimized to extract the frequency andbandwidth of speech resonances with high time-resolution.

FIG. 3 illustrates one embodiment of the invention in additional detail.Generally, speech recognition system 100 includes input processingmodule 110, which is configured to generate speech signal 120, asdescribed above. As illustrated, reconstruction module 210 receivesspeech signal 120. In one embodiment, speech signal 120 is a digitizedspeech signal from a microphone or network source. In one embodiment,speech signal 120 is relatively low in accuracy and sampling frequency,e.g., 8-bit sampling. Reconstruction module 210 reconstructs theacoustic speech resonances using a general model of acoustic resonance.

For example, an acoustic resonance can be mathematically modeled as acomplex exponential:

r(t)=e ^(−2π·β·t) e ^(−i2π·f·t), for t>0  (0.1)

Where f is the frequency of the resonance (in Hertz), and β is thebandwidth (in Hertz). By convention, β is approximately the measureablefull-width-at-half-maximum bandwidth. Further, complex soundtransmission can be well described by a (real) sine wave. The signalcapture process is thus the equivalent of taking the real (or imaginary)part of the complex source, which, however, also loses instantaneousinformation. As described in more detail below, reconstruction module310 recreates the original complex representation of the acoustic speechresonances.

In the illustrated embodiment, reconstruction module 210 includes aplurality of complex filters (CFs) 310. One embodiment of a complexfilter 310 is described in more detail with respect to FIG. 4, below.Generally, reconstruction module 210 produces a plurality ofreconstructed signals, Y_(n), each of which includes a real part (Y_(R))and an imaginary part (Y_(I)).

As shown, system 100 includes an estimator module 220, which in theillustrated embodiment includes a plurality of estimator modules 320,each of which is configured to receive a reconstructed signal Y_(n). Inthe illustrated embodiment, each estimator module 320 includes anintegration kernel 322. In an alternate embodiment, module 220 includesa single estimator module 320, which can be configured with one or moreintegration kernels 322. In an alternate embodiment, estimator module320 does not include an integration kernel 322.

Generally, estimator modules 320 generate estimated instantaneousfrequencies and bandwidths based on the reconstructed signals using theproperties of an acoustic resonance. The equation for a complex acousticresonance described above can be reduced to a very simple form:

r(t)=e ^(−at), with a=2πβt+i2πf  (0.2)

for a resonance at frequency f, with bandwidth β. An equation of thefamily e^(−at) can also be modeled by a difference equation,

y[t]=(1−a)·y[t−1]+x[t]  (0.3)

for a forcing function x. And if x(t)is zero, as in a ringing responseof the vocal tract resonances to an impulse from the glottal pulse, forexample, in one embodiment, system 100 can determine the coefficient abased on two samples of a reconstructed resonance y, and from thecoefficient a, the frequency and bandwidth can be estimated, asdescribed in more detail below. In an alternate embodiment, alsodescribed in more detail below, where x is variable, or in noisyoperating environment, system 100 can calculate auto-regression resultsto determine the coefficient a.

In the illustrated embodiment, each estimator module 320 passes theresults of its frequency and bandwidth estimation to analysis andcorrection module 230. Generally, module 230 receives a plurality ofinstantaneous frequency and bandwidth estimates and corrects theseestimates, based on certain configurations, described in more detailbelow.

As shown, module 130 produces an output 340, which, in one embodiment,system 100 sends to post processing module 140 for additionalprocessing. In the embodiment, output 340 is a plurality of frequenciesand bandwidths.

Thus, generally, system 100 receives a speech signal including aplurality of speech resonances, reconstructs the speech resonances,estimates their instantaneous frequency and bandwidth, and passesprocessed instantaneous frequency and bandwidth information on to apost-processing module for further processing, analysis, andinterpretation. As described above, the first phase of analysis andprocessing is reconstruction, shown in more detail of one embodiment inFIG. 4.

FIG. 4 is a block diagram illustrating operation of a complex gammatonefilter 310 in accordance with one embodiment. Specifically, filter 310receives input speech signal 120, divides speech signal 120 into twosecondary input signals 412 and 414, and passes the secondary inputsignals 412 and 414 through a series of filters 420. In the illustratedembodiment, filter 310 includes a single series of filters 420. In analternate embodiment, filter 310 includes one or more additional seriesof filters 420, arranged (as a series) in parallel to the illustratedseries.

In the illustrated embodiment, the series of filters 420 is four filterslong. So configured, the first filter 420 output serves as the input tothe next filter 420, which output serves as the input to the next filter420, and so forth.

In one embodiment, each filter 420 is a complex quadrature filterconsisting of two filter sections 422 and 424. In the illustratedembodiment, filter 420 is shown with two sections 422 and two sections424. In an alternate embodiment, filter 420 includes a single section422 and a single section 424, each configured to operate as describedbelow. In one embodiment, each filter section 422 and 424 is a circuitconfigured to perform a transform on its input signal, described in moredetail below. Each filter section 422 and 424 produces a real numberoutput, one of which applies to the real part of the filter 420 output,and the other of which applies to the imaginary part of the filter 420output.

In one embodiment, filter 420 is a finite impulse response (FIR) filter.In one embodiment, filter 420 is an infinite impulse response (IIR)filter. In a preferred embodiment, the series of four filters 420 is acomplex gammatone filter, which is a fourth-order gamma functionenvelope with a complex exponential. In an alternate embodiment,reconstruction module 310 is configured with other orders of the gammafunction, corresponding to the number of filters 420 in the series.

Generally, the fourth-order gammatone filter impulse response is afunction of the following terms:

-   -   g_(n)(t)=Complex gammatone filter n    -   b_(n)=Bandwidth parameter of filter n    -   f_(n)=Center frequency of filter n

and is given by:

g _(n)(t)=t ³ e ^(−2π·b) ^(n) ^(·t) e ^(−2π·f) ^(n) ^(·t), fort>0  (0.4)

As such, in one embodiment, the output of filter 420 is an output of Ncomplex numbers at the sampling frequency. Accordingly, the use ofcomplex-valued filters eliminates the need to convert a real-valuedinput single into its analytic representation, because the response of acomplex filter to a real signal is also complex. Thus, filter 310provides a distinct processing advantage as filter 420 can be configuredto unify the entire process in the complex domain.

Moreover, each filter 420 can be configured independently, with a numberof configuration options, including the filter functions, filter windowfunctions, filter center frequency, and filter bandwidth for each filter420. In one embodiment, the filter center frequency and/or filterbandwidth are selected from a predetermined range of frequencies and/orbandwidths. In one embodiment, each filter 420 is configured with thesame functional form. In a preferred embodiment, each filter isconfigured as a fourth-order gamma envelope.

In one embodiment, each filter 420 filter bandwidth and filter spacingare configured to optimize overall analysis accuracy. As such, theability to specify the filter window function, center frequency, andbandwidth of each filter individually contributes significantflexibility in optimizing filter 310, particularly so as to analyzespeech signals. In the preferred embodiment, each filter 420 isconfigured with 2% center frequency spacing and filter bandwidth ofthree-quarters of the center frequency (with saturation at 500 Hz). Inone embodiment, filter 310 is a fourth-order complex gammatone filter,implemented as a cascade of first-order gammatone filters 420 inquadrature.

The following is a mathematic justification for using a cascade offirst-order gammatone filters to create a fourth-order gammatone filter.For a complex input x=x_(R)+ix_(I), the complex kernel of thefirst-order complex gammatone filter 420 can be represented asg=g_(R)+ig_(I), where,

g _(R)(τ)=e ^(−2πbτ)cos 2πfτ

g _(I)(τ)=e ^(−2πbτ)sin 2πfτ  (0.5)

In one embodiment, filter sections 422 and 424 are configuredrespectively, with input signal s, as follows:

G _(R)(s)=∫g _(R)(τ)s(t−τ)dτ

G _(I)(s)=∫g _(I)(τ)s(t−τ)dτ  (0.6)

which, when combined, perform a first-order complex gammatone filterwith output y=y_(R)+iy_(I):

y _(R)(t)=G _(R)(x _(R))−G _(I)(x _(I))

y _(I)(t)=G _(I)(x _(R))+G _(R)(x _(I))  (0.7)

As such, in one embodiment, a fourth-order complex gammatone filter isfour iterations of the first-order filter 420:

G ₄(x)=G ₁ ∘G ₁ ∘G ₁ ∘G ₁(x)  (4.4)

In the illustrated embodiment, for example, each filter 420 isconfigured as a first order gammatone filter. Specifically, filter 310receives an input signal 120, and splits the received signal intodesignated real and imaginary signals. In the illustrated embodiment,splitter 410 splits signal 120 into a real signal 412 and an imaginarysignal 414. In an alternate embodiment, splitter 410 is omitted andfilter 420 operates on signal 120 directly. In the illustratedembodiment, both real signal 412 and “imaginary” signal 414 arereal-valued signals, representing the complex components of input signal120.

In the illustrated embodiment, real signal 412 is the input signal to areal filter section 422 and an imaginary filter 424. In the illustratedembodiment, section 422 calculates G_(R) from signal 412 and section 424calculates G_(I) from signal 412. Similarly, imaginary signal 414 is theinput signal to a real filter section 422 and an imaginary filtersection 424. In the illustrated embodiment, section 422 calculates G_(R)from signal 414 and section 424 calculates G_(I) from signal 414.

As shown, filter 420 combines the outputs from sections 422 and 424.Specifically, filter 420 includes a signal subtractor 430 and a signaladder 432. In the illustrated embodiment, subtractor 430 and adder 432are configured to subtract or add the signal outputs from sections 422and 424. One skilled in the art will understand that there are a varietyof mechanisms suitable for adding and/or subtracting two signals. Asshown, subtractor 430 is configured to subtract the output of imaginaryfilter section 424 (to which signal 414 is input) from the output ofreal filter section 422 (to which signal 412 is input). The output ofsubtractor 430 is the real component, Y_(R), of the filter 420 output.

Similarly, adder 432 is configured to add the output of imaginary filtersection 424 (to which signal 412 is input) to the output of real filtersection 422 (to which signal 414 is input). The output of adder 432 isthe real value of the imaginary component, Y_(I), of the filter 420output. As shown, module 400 includes four filters 420, the output ofwhich is a real component 440 and an imaginary component 442. Asdescribed above, real component 440 and imaginary component 442 arepassed to an estimator module for further processing and analysis.

Returning now to FIG. 3, in the illustrated embodiment of system 100,estimator module 220 includes a plurality of estimator modules 320. Asdescribed above, each estimator module 320 receives a real component(Y_(R)) and a (real-valued) imaginary component (Y_(I)) fromreconstruction module 310. In one embodiment, each estimator module 320receives or is otherwise aware of the configuration of the particularcomplex filter 310 that generated the input to that estimator module320. In one embodiment, each estimator module 320 is associated with acomplex filter 310, and is aware of the configuration setting of thecomplex filter 310, including the filter function(s), filter centerfrequency, and filter bandwidth.

In the illustrated embodiment, each estimator module 320 also includesan integration kernel 322. In an alternate embodiment, each estimatormodule 320 operates without an integration kernel 322. In oneembodiment, at least one integration kernel 322 is a second order gammaIIR filter. Generally, each integration kernel 322 is configured toreceive real and imaginary components as inputs, and to calculatezero-lag delays and variable-lag delays based on the received inputs.

Each estimator module 320 uses variable-delays of the filtered signalsto form a set of products to estimate the frequency and bandwidth usingmethods described below. There are several embodiments of the estimatormodule 320; for example, the estimator module 320 may contain anintegration kernel 322, as illustrated. For clarity, three alternativeembodiments of the system with increasing levels of complexity areintroduced here.

In the first embodiment, each estimator module 320 generates anestimated frequency and an estimated bandwidth of a speech resonance ofthe input speech signal 120 without an integration kernel 322. Theestimated frequency and bandwidth are based only on the current filteredsignal output from the CF 310 associated with that estimator module 320,and a single-lag delay of that filtered signal output. In oneembodiment, the plurality of filters 310 and associated estimatormodules 320 generate a plurality of estimated frequencies and bandwidthsat each time sample.

In a second embodiment, each estimator module 320 includes anintegration kernel 322, which forms an integrated-product set. Based onthe integrated-product set, estimator module 320 generates an estimatedfrequency and an estimated bandwidth of a speech resonance of the inputspeech signal 120. Each integration kernel 322 forms theintegrated-product set by updating products of the filtered signaloutput and a single-delay of the filtered signal output for the lengthof the integration. In one embodiment, the plurality of filters 310 andassociated estimator modules 320 generate a plurality of estimatedfrequencies and bandwidths at each time sample, which are smoothed overtime by the integration kernel 322.

In a third embodiment, the integrated-product set has anat-least-two-lag complex product, increasing the number of products inthe integrated-product set. These three embodiments are described inmore detail below.

In the first embodiment introduced above, estimator module 320 computesa single-lag product set using the output of a CF 312 withoutintegration kernel 322. In this embodiment, the product set{y[y]y*[t−1], |y[t]|²}, where y is the complex output of CF 312, is usedto find the instantaneous frequency and bandwidth of the input speechsignal 302 using a single delay, extracting a single resonance at eachpoint in time. Estimator module 320 computes the instantaneous frequency{circumflex over (f)} and instantaneous bandwidth {circumflex over (β)}with the single-lag product set using the following equations:

$\begin{matrix}{{\hat{f} = {2\pi \; {{dt} \cdot {\arg ( \frac{{y\lbrack t\rbrack}{y^{*}\lbrack {t - 1} \rbrack}}{{{y\lbrack t\rbrack}}^{2}} )}}}}{\hat{\beta} = {{- \frac{1}{2\pi \; {dt}}}{\ln ( \frac{{y\lbrack t\rbrack}{y^{*}\lbrack {t - 1} \rbrack}}{{{y\lbrack t\rbrack}}^{2}} )}}}} & (0.8)\end{matrix}$

where dt is the sampling interval. In a preferred embodiment, one ormore estimator modules 320 calculate the instantaneous frequency andbandwidth from a single-lag product set based on each CF 312 output.

In alternate embodiments (e.g., the second and third embodimentsintroduced above), estimator module 320 computes an integrated-productset of variable delays using integration kernel 322. Theintegrated-product set is used to compute the instantaneous frequencyand bandwidth of the speech resonances of the input speech signal 302.In a preferred embodiment, one or more estimator modules 320 calculatean integrated-product set based on each CF 312 output.

The integrated-product set of the estimator module 320 can includezero-lag products, single-lag products, and at-least-two lag productsdepending on the embodiment. In these embodiments, theintegrated-product set is configured as an integrated-product matrixwith the following definitions:

-   -   Φ_(N)(t)=Integrated-product matrix with N delays    -   φ_(m,n)(t)=Integrated-product matrix element with delays m, n<N    -   y=Complex-signal output of CF 312 in Reconstruction module 310    -   k=Integration kernel 322 within Estimator module 320        Estimator module 320 updates the elements of the        integrated-product matrix at each sampling time, with        time-integration performed separately for each element over a        integration kernel k[τ] of length l,

$\begin{matrix}{{\phi_{m,n}(t)} \equiv {\sum\limits_{\tau = 0}^{l}\; {{k\lbrack\tau\rbrack}{y\lbrack {t - \tau - m} \rbrack}{y^{*}\lbrack {t - \tau - n} \rbrack}}}} & (0.9)\end{matrix}$

The full integrated-product set with N-delays is an N+1-by-N-N+1 matrix:

$\begin{matrix}{\Phi_{N} = \begin{bmatrix}\phi_{0,0} & \ldots & \phi_{0,N} \\\; & \ldots & \; \\\phi_{N,0} & \ldots & \phi_{N,N}\end{bmatrix}} & (0.10)\end{matrix}$

As such, for a maximum delay of 1 (i.e. a single-lag), the integratedproduct set is a 2×2 matrix:

$\begin{matrix}{\Phi_{1} = \begin{bmatrix}\phi_{0,0} & \phi_{0,1} \\\phi_{1,0} & \phi_{1,1}\end{bmatrix}} & (0.11)\end{matrix}$

Accordingly, element φ_(0,0) is a zero-lag complex product and elementsφ_(0,1), φ_(1,1), and, φ_(1,0) are single-lag complex products.Additionally, for a maximum delay of 2 (i.e., an at-least-two-lag), theintegrated-product set is a 3×3 matrix, composed of the zero-lag andsingle-lag products from above, as well as an additional column and rowof two-lag products: φ_(0,2), φ_(1,2), φ_(2,2), φ_(2,1), and, φ_(2,0).Generally, additional lags improve the precision of subsequent frequencyand bandwidth estimates. One skilled in the art will understand thatthere is a computational trade-off between precision gained byadditional lags and the power/time required to compute the additionalelements.

In this embodiment, estimator module 320 is configured to usetime-integration to calculate the integrated-product set. Generally,complex time-integration provides flexible optimization for estimates ofspeech resonances. For example, time-integration can be used to averageresonance estimates over the glottal period to obtain more accurateresonance values, independent of glottal forcing.

Function k is chosen to optimize the signal-to-noise ratio whilepreserving speed of response. In a preferred embodiment, the integrationkernel 322 configures k as a second-order gamma function. In oneembodiment, integration kernel 322 is a second-order gamma IIR filter.In an alternate embodiment, integration kernel 322 is an otherwiseconventional FIR or IIR filter.

In the second embodiment with a single-delay integrated-product set,introduced above, the estimator module 320 calculates the instantaneousfrequency {circumflex over (f)} and instantaneous bandwidth {circumflexover (β)} using elements of the single-delay integrated-product matrixwith the following equations:

$\begin{matrix}{{\hat{f} = {2\pi \; {{dt} \cdot {\arg ( {\phi_{1,0}/\phi_{1,1}} )}}}}{\hat{\beta} = {{- \frac{1}{2\pi \; {dt}}}{\ln ( {\phi_{1,0}/\phi_{1,1}} )}}}} & (0.12)\end{matrix}$

In this embodiment, {circumflex over (β)} is the estimated bandwidthassociated with a pole-model of a resonance. One skilled in the art willunderstand that other models can also be employed.

It is worth nothing that these equations for frequency and bandwidthestimation are equivalent to the equations in the first embodimentdescribed above, where the integration window k is configured as aKronecker delta function, essentially removing the integration kernel,resulting in the equivalent product matrix elements:

φ_(m,n)(t)≡y[t−m]y*[t−n]  (0.13)

In the third embodiment introduced above, estimator module 320 uses anintegrated product-set with additional delays to estimate the propertiesof more resonances per complex filter at each sample time. This can beused in detecting closely-spaced resonances.

In summary, reconstruction module 310 provides an approximate complexreconstruction of an acoustic speech signal. Estimator modules 320 usethe reconstructed signals that are the output of module 310 to computethe instantaneous frequency and bandwidth of the resonance, based inpart on the properties of acoustic resonance generally.

In the illustrated embodiment, analysis and correction module 330receives the plurality of estimated frequencies and bandwidths, as wellas the product sets from the estimator modules 320. Generally, analysis& correction module 330 provides an error estimate of the frequency andbandwidth calculations using regression analysis. The analysis &correction module uses the properties of the filters in recognitionmodule 310 to produce one or more corrected frequency and bandwidthestimates 340 for further processing, analysis, and interpretation.

In one embodiment, analysis & correction module 330 processes the outputof the integrated-product set as a complex auto-regression problem. Thatis, module 330 computes the best difference equation model of thecomplex acoustic resonance, adding a statistical measure of fit. Moreparticularly, in one embodiment, analysis & correction module 330calculates an error estimate from the estimation modules 320 using theproperties of regression analysis in the complex domain with thefollowing equation:

$\begin{matrix}{r^{2} = \frac{\phi_{0,0} - {\phi_{1,1} \cdot {{\phi_{1,0}/\phi_{1,1}}}^{2}}}{\phi_{0,0}}} & (0.14)\end{matrix}$

The error r is a measure of the goodness-of-fit of the frequencyestimate. In one embodiment, module 330 uses r to identify instantaneousfrequencies resulting from noise versus those resulting from resonance.Use of this information in increasing the accuracy of the estimates isdiscussed below.

In addition to an error estimate, an embodiment of analysis & correctionmodule 330 also estimates a corrected instantaneous bandwidth of aresonance by using the estimates from one or more estimator modules 320.In a preferred embodiment, module 330 estimates the correctedinstantaneous bandwidth using pairs of frequency estimates, asdetermined by estimator modules 320 with corresponding complex filters312 closely spaced in center frequency. Generally, this estimate betterapproximates the bandwidth of the resonance than the single-filter-basedestimates described above.

Specifically, module 330 can be configured to calculate a more accuratebandwidth estimate using the difference in frequency estimate over thechange in center frequency across two adjacent estimator modules,

$\begin{matrix}{v_{n} = \frac{{\hat{f}}_{n + 1} - {\hat{f}}_{n}}{f_{n + 1} - f_{n}}} & (0.15)\end{matrix}$

The corrected instantaneous bandwidth estimate from the n^(th) estimatormodule 320, {circumflex over (β)}_(n), can be estimated using theselected bandwidth of the corresponding complex filter 312, b_(n), withthe following equation:

$\begin{matrix}{{\hat{\beta}}_{n} = {a_{0}{v_{n}( \frac{1 + {a_{1}v_{n}} - {a_{2}v_{n}^{2}}}{1 + {a_{3}v_{n}} - {a_{4}v_{n}^{2}}} )}b_{n}}} & (0.16)\end{matrix}$

where, in one embodiment, the preferred coefficients, found empirically,are:

-   -   a₀=6.68002    -   a₁=3.69377    -   a₂=2.87388    -   a₃=47.5236    -   a₄=42.4272

In one embodiment, in particular where each CF 312 is a complexgammatone filter, the estimated instantaneous frequency can be skewedaway from the exact value of the original resonance, in part because ofthe asymmetric frequency response of the complex filters 312. Thus,module 330 can be configured to use the corrected bandwidth estimate,obtained using procedures described above, to correct errors in theestimated instantaneous frequencies coming from the estimator modules320. For example, in one embodiment, for a CF 312 with center frequencyf, bandwidth b, and uncorrected frequency estimate {circumflex over(f)}, the best-fit equation for frequency estimate correction is:

{circumflex over (f)} _(corrected) =f+(1+3.92524·R ²)·({circumflex over(f)}−f−c ₁ R ^(c) ² ·e ^(−c) ³ ^(R))  (0.17)

where R={circumflex over (β)}/b is the ratio of estimated resonancebandwidth to filter bandwidth. In one embodiment, the constants arefound empirically. For example, where b<500:

-   -   c₁=0.059101+0.816002·f    -   c₂=2.3357    -   c₃=3.58372        and for b=500:

c₁ = 0.513951 + 140340.0/(−409.325 + f)c₂ = 1.95121 + 145.771/(−292.151 + f)c₃ = 1.72734 + 654.08/(−319.262 + f)

As such, analysis and correction module 230 can be configured to improvethe accuracy of the estimated resonance frequency and bandwidthgenerated by the estimator modules 320. Thus, the improved estimates canbe forwarded for speech recognition processing and interpretation, withimproved results over estimates generated by prior art approaches.

For example, in one embodiment, post-processing module 140 performsthresholding operations on the plurality of estimates received fromanalysis & correction modules 230. In one embodiment, thresholdingoperations discard estimates outside a predetermined range in order toimprove signal-to-noise performance. In one embodiment, module 140aggregates the received estimates to reduce the over-determineddata-set. One skilled in the art will understand that module 140 can beconfigured to employ other suitable post-processing operations.

Thus, generally, system 100 can be configured to perform all threestages of speech signal process and analysis described above, namely,reconstruction, estimation, and analysis/correction. The following flowdiagrams describe these stages in additional detail. Referring now toFIG. 5, the illustrated process begins at block 505, in an input captureand pre-processing stage, wherein the speech recognition system receivesa speech signal. For example, reconstruction module 210 receives aspeech signal from input processing module 202 (of FIG. 2).

Next, the process enters the processing and analysis stage.Specifically, as indicated at block 510, reconstruction module 210reconstructs the received speech signal. Next, as indicated at block515, estimator module 220 estimates the frequency and bandwidth of aspeech resonance of the reconstructed speech signal. Next, as indicatedat block 520, analysis and correction module 230 performs analysis andcorrection operations on the estimated frequency and bandwidth of thespeech resonance.

Next, the process enters the post-processing stage. Specifically, asindicated at block 525, post-processing module 140 performspost-processing on the corrected frequency and bandwidth of the speechresonance. Particular embodiments of this process are described in moredetail below.

Referring now to FIG. 6, the illustrated process begins at block 505, asabove. Next, as indicated at block 610, reconstruction module 210generates a plurality of filtered signals based on a speech resonancesignal of the received speech signal received as described in block 505.In the preferred embodiment, each of the plurality of filtered signal isa reconstructed (real and complex) speech signal, as described above.

Next, as indicated at block 615, estimator module 220 selects one of thefiltered signals generated as described in block 610. Next, as indicatedat block 620, estimator module 220 generates a single-lag delay of aspeech resonance of the selected filtered signal.

Next, as indicated at block 625, estimator module 220 generates a firstestimated frequency of the speech resonance based on the filtered signaland the single-lag delay of the selected filtered signal. Next, asindicated at block 630, estimator module 220 generates a first estimatedbandwidth of the speech resonance based on the filtered signal and thesingle-lag delay of the selected filtered signal. Thus, flow diagram 600describes a process that generates an estimated frequency and bandwidthof a speech resonance of a speech signal.

Referring now to FIG. 7, the illustrated process advances as describedabove as indicated in blocks 505, 610, and 615. Next, as indicated atblock 720, estimator module 220 generates at least one zero-lagintegrated complex product based on the filtered signal selected asdescribed in block 615. Next, as indicated at block 725, estimatormodule 220 generates at least one single-lag integrated complex productbased on the selected filtered signal.

Next, as indicated at block 730, estimator module 220 generates a firstestimated frequency based on the zero-lag and single-lag integratedcomplex products. Next, as indicated at block 735, estimator module 220generates a first estimated bandwidth based on the zero-lag andsingle-lag integrated complex products.

Referring now to FIG. 8, the illustrated process advances as describedabove as indicated in blocks 505, 610, 615, and 720. Next, as indicatedat block 825, estimator module 220 generates at least oneat-least-two-lag integrated complex product based on the selectedfiltered signal.

Next, as indicated at block 830, estimator module 220 generates a firstestimated frequency based on the zero-lag and at-least-two-lagintegrated complex products. Next, as indicated at block 835, estimatormodule 220 generates a first estimated bandwidth based on the zero-lagand at-least-two-lag integrated complex products.

Referring now to FIG. 9, the illustrated process begins as describedabove as indicated in block 505. Next, as indicated at block 910,reconstruction module 210 selects a first and second bandwidth. Asdescribed above, in one embodiment, reconstruction module 210 selects afirst bandwidth, used to configure a first complex filter, and a secondbandwidth, used to configure a second complex filter.

Next, as indicated at block 915, reconstruction module 210 selects afirst and second center frequency. As described above, in oneembodiment, reconstruction module 210 selects a first center frequency,used to configure the first complex filter, and a second centerfrequency, used to configure the second complex filter. Next, asindicated at block 920, reconstruction module 210 generates a first andsecond filtered signal. As described above, in one embodiment, the firstfilter generates the first filtered signal and the second filtergenerates the second filtered signal.

Next, as indicated at block 925, estimator module 220 generates a firstand second estimated frequency. As described above, in one embodiment,estimator module 220 generates a first estimated frequency based on thefirst filtered signal, and generates a second estimated frequency basedon the second filtered signal.

Next, as indicated at block 930, estimator module 220 generates a firstand second estimated bandwidth. As described above, in one embodiment,estimator module 220 generates a first estimated bandwidth based on thefirst filtered signal, and generates a second estimated bandwidth basedon the second filtered signal.

Next, as indicated at block 935, analysis and correction module 230generates a third estimated bandwidth based on the first and secondestimated frequencies, the first and second center frequencies, and thefirst selected bandwidth. Next, as indicated at block 940, analysis andcorrection module 230 generates a third estimated frequency based on thethird estimated bandwidth, the first estimated frequency, the firstcenter frequency, and the first selected bandwidth.

Other modifications and implementations will occur to those skilled inthe art without departing from the spirit and scope of the invention asclaimed. Accordingly, the above description is not intended to limit theinvention except as indicated in the following claims.

1. A method for determining an instantaneous frequency and aninstantaneous bandwidth of a speech resonance of a speech resonancesignal, the method comprising: receiving a speech resonance signalhaving a real component; filtering the speech resonance signal so as togenerate a plurality of filtered signals such that the real componentand an imaginary component of the speech resonance signal arereconstructed; and generating a first estimated frequency and a firstestimated bandwidth of a speech resonance of the speech resonance signalbased on a first filtered signal of the plurality of filtered signalsand a single-lag delay of the first filtered signal.
 2. The method ofclaim 1, wherein: filtering is performed by a filter bank having aplurality of complex filters, each complex filter generating one of theplurality of filtered signals.
 3. The method of claim 1, furthercomprising: generating a plurality of estimated frequencies and aplurality of estimated bandwidths, based on the plurality of filteredsignals and a plurality of single-lag delays of the plurality offiltered signals.
 4. The method of claim 1, wherein the filter bankincludes a plurality of finite impulse response (FIR) filters.
 5. Themethod of claim 1, wherein the filter bank includes a plurality ofinfinite impulse response (IIR) filters.
 6. The method of claim 1,wherein the filter bank includes a plurality of complex gammatonefilters.
 7. The method of claim 1, wherein each complex filter includesa first selected bandwidth and a first selected center frequency.
 8. Themethod of claim 1, wherein each complex filter comprises: a selectedbandwidth of a plurality of bandwidths, the plurality of bandwidthsbeing distributed within a first predetermined range; and a selectedcenter frequency of a plurality of center frequencies, the plurality ofcenter frequencies being distributed within a second predeterminedrange.
 9. The method of claim 1, wherein each complex filter comprises:a first selected bandwidth and a first selected center frequency, thefirst selected bandwidth and first selected center frequency beingconfigured to optimize analysis accuracy.
 10. A method for determiningan instantaneous frequency and an instantaneous bandwidth of a speechresonance of a speech resonance signal, the method comprising: receivinga speech resonance signal having a real component; filtering the speechresonance signal so as to generate a plurality of filtered signals suchthat the real component and an imaginary component of the speechresonance signal are reconstructed; forming a first integrated-productset, the forming being performed by an integration kernel, the firstintegrated-product set being based on a first filtered signal of theplurality of filtered signals, and the first integrated-product sethaving: at least one zero-lag complex product and at least onesingle-lag complex product; and generating, based on the firstintegrated-product set, a first estimated frequency and a firstestimated bandwidth of a speech resonance of the speech resonancesignal.
 11. The method of claim 10, further comprising: forming aplurality of integrated-product sets, each integrated-product set beingbased on one of the plurality of filtered signals, and eachintegrated-product set having: at least one zero-lag complex product andat least one single-lag complex product; and generating, based on theplurality of integrated-product sets, a plurality of estimatedfrequencies and a plurality of estimated bandwidths.
 12. The method ofclaim 10, wherein: filtering is performed by a filter bank having aplurality of finite impulse response (FIR) filters.
 13. The method ofclaim 10, wherein: filtering is performed by a filter bank having aplurality of infinite impulse response (IIR) filters.
 14. The method ofclaim 10, wherein: filtering is performed by a filter bank having aplurality of complex gammatone filters.
 15. The method of claim 10,wherein: filtering is performed by a filter bank having a plurality ofcomplex filters, each complex filter generating one of the plurality offiltered signals.
 16. The method of claim 10, wherein: filtering isperformed by a filter bank having a plurality of complex filters, eachcomplex filter having a first selected bandwidth and a first selectedcenter frequency.
 17. The method of claim 10, wherein: filtering isperformed by a filter bank having a plurality of complex filters, eachcomplex filter having: a selected bandwidth of a plurality ofbandwidths, the plurality of bandwidths being distributed within a firstpredetermined range, and a selected center frequency of a plurality ofcenter frequencies, the plurality of center frequencies beingdistributed within a second predetermined range.
 18. The method of claim10, wherein: filtering is performed by a filter bank having a pluralityof complex filters, each complex filter having: a selected bandwidth ofa plurality of bandwidths, the selected bandwidth being configured tooptimize analysis accuracy, and a selected center frequency of aplurality of center frequencies, the selected center frequency beingconfigured to optimize analysis accuracy.
 19. The method of claim 10,wherein: the integration kernel is a second order gamma IIR filter. 20.The method of claim 10, wherein the first filtered signal is formed by afirst filter having a first selected bandwidth and a first centerfrequency, the method further comprising: generating a second estimatedfrequency and a second estimated bandwidth, the generating being basedon a second filtered signal of the plurality of filtered signals, thesecond filtered signal being formed by a second filter having a secondselected bandwidth and a second center frequency; and generating a thirdestimated bandwidth, the generating being based on: the first and secondestimated frequencies, the first selected bandwidth, and the first andsecond center frequencies.
 21. The method of claim 10, wherein the firstfiltered signal is formed by a first filter having a first selectedbandwidth and a first center frequency, the method further comprising:generating a second estimated frequency and a second estimatedbandwidth, the generating being based on a second filtered signal of theplurality of filtered signals, the second filtered signal being formedby a second filter having a second selected bandwidth and a secondcenter frequency; and generating a third estimated bandwidth, thegenerating being based on: the first and second estimated frequencies,the first selected bandwidth, and the first and second centerfrequencies; and generating a third estimated frequency, the generatingbeing based on: the third estimated bandwidth, the first estimatedfrequency, the first selected frequency, and the first selectedbandwidth.
 22. A method for determining an instantaneous frequency andan instantaneous bandwidth of a speech resonance of a speech resonancesignal, the method comprising: receiving a speech resonance signalhaving a real component; filtering the speech resonance signal so as togenerate a plurality of filtered signals such that the real componentand an imaginary component of the speech resonance signal arereconstructed; forming a first integrated-product set, the forming beingperformed by an integration kernel, the first integrated-product setbeing based on a first filtered signal of the plurality of filteredsignals, and the first integrated-product set having: at least onezero-lag complex product, and at least one two-or-more-lag complexproduct; and generating, based on the first integrated-product set, afirst estimated frequency and a first estimated bandwidth of a speechresonance of the speech resonance signal.
 23. The method of claim 22,further comprising: forming a plurality of integrated-product sets, eachintegrated-product set being based on one of the plurality of filteredsignals, and each integrated-product set having: at least one zero-lagcomplex product, and at least one two-or-more-lag complex product; andgenerating, based on the plurality of integrated-product sets, aplurality of estimated frequencies and a plurality of estimatedbandwidths.
 24. The method of claim 22, wherein: filtering is performedby a filter bank having a plurality of finite impulse response (FIR)filters.
 25. The method of claim 22, wherein: filtering is performed bya filter bank having a plurality of infinite impulse response (IIR)filters.
 26. The method of claim 22, wherein: filtering is performed bya filter bank having a plurality of complex gammatone filters.
 27. Themethod of claim 22, wherein: filtering is performed by a filter bankhaving a plurality of complex filters, each complex filter generatingone of the plurality of filtered signals.
 28. The method of claim 22,wherein: filtering is performed by a filter bank having a plurality ofcomplex filters, each complex filter having a first selected bandwidthand a first selected center frequency.
 29. The method of claim 22,wherein: filtering is performed by a filter bank having a plurality ofcomplex filters, each complex filter having: a selected bandwidth of aplurality of bandwidths, the plurality of bandwidths being distributedwithin a first predetermined range, and a selected center frequency of aplurality of center frequencies, the plurality of center frequenciesbeing distributed within a second predetermined range.
 30. The method ofclaim 22, wherein: filtering is performed by a filter bank having aplurality of complex filters, each complex filter having: a selectedbandwidth of a plurality of bandwidths, the selected bandwidth beingconfigured to optimize analysis accuracy, and a selected centerfrequency of a plurality of center frequencies, the selected centerfrequency being configured to optimize analysis accuracy.
 31. The methodof claim 22, wherein: the integration kernel is a second order gamma IIRfilter.
 32. A method for determining an instantaneous frequency and aninstantaneous bandwidth of a speech resonance of a speech resonancesignal, the method comprising: generating a first estimated frequencyand a first estimated bandwidth of the speech resonance based on a firstfiltered signal, the first filtered signal being formed by a firstcomplex filter having a first selected bandwidth and a first centerfrequency; generating a second estimated frequency and a secondestimated bandwidth of the speech resonance based on a second filteredsignal, the second filtered signal being formed by a second complexfilter having a second selected bandwidth and a second center frequency;and generating a third estimated bandwidth of the speech resonance, thegenerating being based on: the first and second estimated frequencies,the first selected bandwidth, and the first and second centerfrequencies.
 33. The method of claim 32, further comprising: generatinga third estimated frequency of the speech resonance, the generatingbeing based on: the third estimated bandwidth, the first estimatedfrequency, the first center frequency, and the first selected bandwidth.34. An apparatus for determining an instantaneous frequency and aninstantaneous bandwidth of a speech resonance of a speech resonancesignal, the apparatus comprising: a reconstruction module configured toreceive a speech resonance signal having a real component, thereconstruction module further configured to filter the speech resonancesignal so as to generate a plurality of filtered signals such that thereal component and an imaginary component of the speech resonance signalare reconstructed; and an estimator module coupled to the reconstructionmodule, the reconstruction module configured to generate a firstestimated frequency and a first estimated bandwidth of a speechresonance of the speech resonance signal based on both a first filteredsignal of the plurality of filtered signals and a single-lag delay ofthe first filtered signal.
 35. The apparatus of claim 34, wherein: thereconstruction module includes a filter bank having a plurality ofcomplex filters, each complex filter being configured to generate one ofthe plurality of filtered signals.
 36. The apparatus of claim 34,wherein the estimator module is further configured to: generate aplurality of estimated frequencies and a plurality of estimatedbandwidths, based on both the plurality of filtered signals and aplurality of single-lag delays of the plurality of filtered signals. 37.The apparatus of claim 34, wherein the reconstruction module includes aplurality of finite impulse response (FIR) filters.
 38. The apparatus ofclaim 34, wherein the reconstruction module includes a plurality ofinfinite impulse response (IIR) filters.
 39. The apparatus of claim 34,wherein the reconstruction module includes a plurality of complexgammatone filters.
 38. The apparatus of claim 34, wherein thereconstruction module includes a plurality of complex filters, eachcomplex filter having a first selected bandwidth and a first selectedcenter frequency.
 39. The apparatus of claim 34, wherein each complexfilter comprises: a selected bandwidth of a plurality of bandwidths, theplurality of bandwidths being distributed within a first predeterminedrange; and a selected center frequency of a plurality of centerfrequencies, the plurality of center frequencies being distributedwithin a second predetermined range.
 40. The apparatus of claim 34,wherein each complex filter comprises: a first selected bandwidth and afirst selected center frequency, the first selected bandwidth and firstselected center frequency being configured to optimize analysisaccuracy.